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This method keyword requests that the dipole electric field polarizabilities (and hyperpolarizabilities, if possible) be computed. No geometry change or derivatives are implied, but this keyword may be combined in the same job with numerical differentiation of forces by specifying both Freq and Polar in the route section. Freq and Polar may not be combined for methods lacking analytic gradients (MP4(SDTQ), QCISD(T), CCSD(T), and so on). Note that Polar is done by default when second derivatives are computed analytically.

The polarizability and hyperpolarizability are presented in the output in the standard orientation in lower triangular and lower tetrahedral order, respectively: αxx, αxy, αyy, αxz, αyz, αzz and βxxx, βxxy, βxyy, βyyy, βxxz, βxyz, βyyz, βxzz, βyzz, βzzz.

Normally, polarizabilities and hyperpolarizabilities are computed using static frequencies. However, frequency-dependent polarizabilities and hyperpolarizabilities [Olsen85, Sekino86, Rice90, Rice91, Rice92] may be computed by including CPHF=RdFreq in the route section and specifying the desired frequency in the input file.

Optical rotations [Rosenfeld28, Condon37, Eyring44, Buckingham67, Buckingham68, Atkins69, Barron71, Charney79, Amos82, Jorgensen88] may also be predicted via the OptRot option [Karna91, Helgaker94, Pedersen95, Kondru98, Stephens01, Mennucci02, Ruud02, Stephens02a, Stephens03]. See [Stephens05,Wilson05,Stephens08] for example applications.

Raman and ROA intensities can be calculated separately from calculation of the force constants and normal modes, to facilitate using a larger basis for these properties as recommended in [Cheeseman11a]. The keyword Polar=Raman (or Polar=ROA) requests that the force constants be picked up from the checkpoint file (i.e., from a previous Freq calculation) and new polarizability derivatives (and the other two tensor derivatives for ROA) be computed and combined with the force constants in predicting intensities and spectra. Test job 931 provides an example of a two-step ROA calculation.


Perform optical rotation calculation. Use CPHF=RdFreq to specify the desired frequencies. Available for HF and DFT only. This option cannot be combined with NMR. Include IOp(10/46=7) in the route section to include the dipole-quadrupole contribution to the dipole-magnetic dipole polarizability in order to compute the full optical rotation tensor [Pedersen95,Barron04]; the latter will be labeled as Optical Rotation G' tensor in the output. Note that doing so does not change the optical rotation.


Do extra frequency-dependent CPHF for dc-SHG (direct current second harmonic generation) hyperpolarizabilities. This option implies CPHF=RdFreq as well.


Equivalent to Polar=(DCSHG,Cubic) to do 2nd hyperpolarizabilities.


Analytically compute the polarizability and the hyperpolarizability when analytic third derivatives are available. This option is the default for method with analytic second derivatives: RHF and UHF, CASSCF, CIS, MP2 and DFT methods. Note that the polarizability is always computed during analytic frequency calculations.


During numerical frequencies using Linda parallelism, run separate displacements on each worker instead of parallelizing each energy+derivative evaluation across the cluster. More efficient, but requires specifying an extra worker on the master node. This is the default if at least 3 Linda workers were specified. NoWorkerPerturbations suppresses this behavior.


Do four displacements instead of two for each degree of freedom during numerical frequencies, polarizabilities, or freq=anharm. This gives better accuracy and less sensitivity to step size at the cost of doing twice as many calculations.


Computes hyperpolarizabilities in addition to polarizabilities for methods with analytic gradients (first derivatives). Computes polarizabilities by double numerical differentiation of the energy for methods without analytic derivatives. EnOnly is a synonym for DoubleNumer.


Numerically differentiate analytic polarizabilities to produce hyperpolarizabilities. Applicable only to methods having analytic frequencies but no analytic third derivatives.


Computes the polarizability as a numerical derivative of the dipole moment (it is the analytic derivative of the energy, of course, not the expectation value in the case of MP2 or CI energies). The default for methods for which only analytic first derivative gradients are available.


Specifies the step size in the electric field to be 0.0001N atomic units (applies to numerical differentiation).


Restarts a numerical calculation from the checkpoint file. A failed Polar calculation may be restarted from its checkpoint file by simply repeating the route section of the original job, adding the Restart option to the Polar keyword. No other input is required.


Compute magnetic susceptibility as well as other properties (see NMR). Available for HF and DFT only.


When computing numerical derivatives, make two displacements in each coordinate. This is the default. FourPoint will make four displacements but only works with Link 106 (Polar=Numer). Not valid with Polar=DoubleNumer.


Compute the dipole polarizabilities (the default).

The following table summarizes the options to Polar that are required to compute polarizabilities and hyperpolarizabilities for the available methods.

Method Capabilities   Polarizability   Hyperpolarizability
Analytic 3rd derivatives (HF, most DFT)   Polar (default=Analytic)   Polar (default=Analytic)
Analytic frequencies (MP2, CIS, …)   Polar (default=Analytic)   Polar=Cubic
Only analytic gradients (CCSD, BD, …)   Polar (default=Numeric)   Polar=DoubleNumer
No analytic derivatives (CCSD(T), …)   Polar (default=DoubleNumer)   N/A

Frequency-dependent polarizabilities and hyperpolarizabilities (i.e., Polar CPHF=RdFreq) are available only for HF and DFT methods.

Frequency-Dependent Properties. The following job will compute frequency-dependent polarizabilities and hyperpolarizabilities using ω=0.1 Hartrees:

# Polar CPHF=RdFreq HF/6-31G(d)

Frequency-dependent calculation: w=0.1

Molecule specification


Performing a frequency-dependent Polar calculation produces the results for the specified frequency following those for the static case within the output. For example, here are the polarizability values for a frequency-dependent job (ω=0.1 Hartree):

 SCF Polarizability for W=    0.000000:
                1             2             3
      1  0.482729D+01
      2  0.000000D+00  0.112001D+02
      3  0.000000D+00  0.000000D+00  0.165696D+02
 Isotropic polarizability for W=    0.000000       10.87 Bohr**3.
 SCF Polarizability for W=    0.100000:
                1             2             3
      1  0.491893D+01
      2  0.000000D+00  0.115663D+02
      3  0.000000D+00  0.000000D+00  0.171826D+02

 Isotropic polarizability for W=    0.100000       11.22 Bohr**3.

A static polarizability calculation would include only the first section. Similar output follows for hyperpolarizabilities and additional properties.

Optical Rotations. Here is the key part of the output for optical rotation jobs (OptRot option). In this case, we have performed a frequency-dependent calculation by including CPHF=RdFreq in the route section and specified a frequency of 589.3 nm:

 Dipole-magnetic dipole polarizability for W=    0.077318:
                 1             2             3
      1  -0.428755D+01 -0.175571D+01  0.000000D+00
      2  -0.552645D+01  0.987070D+01  0.000000D+00
      3   0.000000D+00  0.000000D+00 -0.676292D+00
 w=    0.077318 a.u., Optical Rotation Beta=     -1.6356 au.
 Molar Mass =  172.2694 grams/mole, [Alpha] ( 5893.0 A) = -366.99 deg.

The specific rotation value is highlighted in the example output.

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